Question:


A circular wheel of diameter 35cm makes 100 revolutions in 1 minute.
Calculate the distance covered by the wheel in half an hour. Express your answer in km.

Answer:

Radius of the wheel: 35 / 2 = 17.5 cm
Circumference of the wheel: 2 x Pi x Radius = 2 x 3.14 x 17.5 cm = 109.9 cm
Distance covered by the wheel in 1 minute = 109.9 x 100 = 10990 cm
Distance covered by the wheel in half an hour = 10990 x 30 = 329700 cm = 3.297 km

Thanks, Ender, for pointing out the mistake. Fixed now.

A box of pens was divided equally among 32 children.8 of these children gave up 2/5 of their share. As a result, the remaining children each received 4 more pens. How many pens were there in the box?


There are 24 remaining children. Each got 4 more pens.
So they got 24 x 4 = 96 pens altogether.
These 96 pens came from 8 children, so each child gave up 96/8 = 12 pens.
This was 2/5 of their share, so each child had 5 x 12 / 2 = 30 pens at first.
All the children had 32 x 30 = 960 pens at first.
There were 960 pens in the box.

Answer: There were 960 pens in the box.

Amos, Ben and Charles shared the cost of a present. Amos and Ben paid 5/9 of the price of the present. Amos and Charles paid 2/3 of the price of the present. Amos paid $4. How much did the present cost?


Amos and Ben paid 5/9. This means Charlie paid 4/9.
Amos and Charlie paid 2/3. This means Ben paid 1/3.
Now, we can work out Amos' share. Charlie and Ben paid 4/9 + 1/3 = 7/9 altogether, so Amos share is 2/9. The present cost 9/2 x 4 = $18.

Question:


Eunice, Grace and Joyce collect badges as their hobby. At first,
Eunice gave 2/5 of her badges to Grace. Grace then gave 3/8 of what
she had to Joyce. Then Joyce gave 1/6 of what she had to Eunice. In
the end, they had 150 badges each. How many badges did Eunice
have at first?



Answer:

We work backwards, beginning with each of them having 150 badges in the end.

In the end:

Eunice: 150
Grace: 150
Joyce: 150

Last transfer: Joyce gave 1/6 of what she had to Eunice.

Joyce had 150 after she gave 1/6 of her badges to Eunice.
So 150 is 5/6 of her badges. She had 150 * 6 / 5 = 180 badges before, and gave 30 to Eunice.
Before Joyce gave her badges to Eunice, the girls had

Eunice: 150 - 30 = 120 (she had 30 fewer badges before)
Grace: 150 (unchanged)
Joyce: 150 + 30 = 180 (she had 30 more badges before)

Second last transfer: Grace gave 3/8 of what she had to Joyce.

Grace had 150 after she gave 3/8 of her badges to Joyce.
So 150 is 5/8 of her badges. She had 150 * 8 / 5 = 240 badges before, and gave 90 to Joyce.
Before Grace gave some of her badges to Joyce, the girls had

Eunice: 120 (unchanged)
Grace: 150 + 90 = 240 (she had 90 more badges before)
Joyce: 180 - 90 = 90 (she had 90 fewer badges before)

First transfer: Eunice gave 2/5 of her badges to Grace.

She had 120 badges after she gave 2/5 to Grace, so 120 is 3/5 of her badges before the transfer.
She had 120 * 5 / 3 = 200 badges before the transfer, and she gave 80 badges to Grace.

Before Eunice gave some of her badges to Grace, the girls had

Eunice: 120 + 80 = 200 (she had 80 more badges before)
Grace: 240 - 80 = 160 (she had 80 fewer badges before)
Joyce: 90 (unchanged)

Answer: Eunice had 200 badges at first.

Question:


Catherine had some money at first. She gave 1/4 of her money to
Anne. As a result, Anne had thrice as much as before. Then, Anne
gave 1/2 of her money to Bernard. Bernard then had 1 1/2 times as
much money as before. Anne still had $129 left. How much money
did each child have at first?

Answer:

Anne

We work backwards for Anne. She had $129 at the end.
This was after giving half her money to Bernard. So, she gave $129 to Bernard.
Before giving $129 to Bernard, she had $129 + $129 = $258.
Anne tripled her money after getting 1/4 of Catherine's money.
So Anne had $258/3 = $86 at first.

Anne had $86 at first

Catherine

Anne tripled her money after getting 1/4 of Catherine's money.
As Anne had $86 at first, she received 2 x $86 = $172 from Catherine.
This was 1/4 of Catherine's money
So Catherine had $172 x 4 = $688 at first

Catherine had $172 x 4 = $688 at first

Bernard

Bernard received $129 from Anne, and had 1 1/2 times as much as before.
So the $129 was half what he had at first.
So Bernard had $129 x 2 = $258 at first.

Bernard had $129 x 2 = $258 at first

Hi XYZ1,


I suggest, err on the side of caution, and use the ‘se’ form as a rule.

Take care.

Question:


There are 2617 vehicle in a carpark
The number of lorries was 353 less than the number of vans but 562 more than the total number of cars and motorcycles. The motorcycles and cars have 1150 wheels altogether. How many cars are there in the carpark?


Answer and approach are the same as Ender's, just added a box model. A few words on Ender's very good strategy first. It breaks up the question into two parts. Both parts are straightforward. The first part is a box model. He uses this to get the total number of cars and motorcycles. He then uses this number for part 2, which is another standard question that he answers with a \"supposition\" or \"assumption\" method.

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PlayfulFairy:

Please help me with these sums.. Thanks !


1) Mdm Siti made some jellies. She gave 4 less than 50% of all the jellies to her mother. She also gave 6 more than 1/4 of the rest of the jellies to her friends. She then had 15 jellies left. How many jellies did she make together at first ? (48 jellies)

Hi PlayfulFairy,

We are given some numbers, 50% and 1/4. So let's divide the jellies into quarters. So we have 4u jellies to start with.

She gave 4 less than half to her mother.
This means Siti's mother has 2u - 4 jellies.
So, Siti has 4u - (2u - 4) = 2u + 4 jellies left.

1 / 4 of the remainder is (2u + 4) / 4 = u/2 + 1
Siti gave 6 more than this to her friends.
So her friends have u/2 + 1 + 6 = u/2 + 7 jellies.

Siti has 15 jellies left.

All the jellies = Jellies to mother + Jellies to friends + Jellies left
4u = (2u - 4) + (u/2 + 7) + 15

Bringing all the us to the left hand side
4u - 2u - u/2 = 15 + 7 - 4
3u / 2 = 18
u = 12

So, all the jellies are 4u = 4 x 12 = 48 jellies.

MathWithModels

alfretztay:

MathWithModels:

[quote=\"Daddy\"]
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[/quote]Yes, sorry. I was careless in part b. Thanks for the correction, alfretztay!

MathWithModels.

Daddy:

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We have two ratios here, but they are ratios of two different numbers. This is the units and parts pattern, and this is the way I'll do it. It's not the only way.

We use units for Jane and parts for Dinah.

Jane (from 25%) 1u : 3u
Dinah (from 50%) 1p : 1p

The total number of red and blue beads doesn't change.

Red beads: 3u + 1p = 610
Blue beads: 1u + 1p = 390

[u][u][u][p]
[----610----]

[u][p]
[390]

[u][p] is common to top and bottom, and it adds up to 390. The top becomes

[u][u]
[220]

which means u = 110. Jane has 4u altogether so this is 440 beads.

a. Jane has 440 beads in the end.

Now for part b.

Dinah has p blue beads in the end
[u][p] is 390, and u is 110, which makes p 390 - 110 = 280
She started with 220 beads, so she received 280 - 220 = 60 beads from Jane.

b. Dinah received 60 beads from Jane.

MathWithModels